NDLI: Heat and gravitation. II. Stability

Content Provider	Springer Nature Link
Author	Frønsdal, Christian
Copyright Year	2010
Abstract	Some features of hydro- and thermodynamics, as applied to atmospheres and to stellar structures, are puzzling. 1. The suggestion, first made by Laplace, that our atmosphere has an adiabatic temperature distribution, is confirmed for the lower layers, but the reason why it should be so is difficult to understand. 2. The standard treatment of relativistic thermodynamics does not allow for a systematic treatment of mixtures, such as the mixture of a perfect gas with radiation. 3. The concept of mass in applications of general relativity to stellar structures is less than completely satisfactory. 4. Arguments in which a concept of energy plays a role, in the context of hydro-thermodynamical systems and gravitation, are not always convincing. It was proposed that a formulation of thermodynamics as an action principle may be a suitable approach to adopt for a new investigation of these matters. In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on ad hoc definitions of the “energy”. We introduce a new virial principle that is formulated entirely within the Eulerian description of hydrodynamics, which allows a simpler derivation of a well known stability criterion for polytropic stellar configurations. Boundary conditions are based entirely on mass conservation. The new approach is tested on isothermal and polytropic atmospheres and then used to initiate a new study of stars. Traditional results for polytropic, spherical configurations are confirmed, but our study gives new insight and new results for the case that radiation is taken into account.
Starting Page	107
Ending Page	126
Page Count	20
File Format	PDF
ISSN	00017701
Journal	General Relativity and Gravitation
Volume Number	43
Issue Number	1
e-ISSN	15729532
Language	English
Publisher	Springer US
Publisher Date	2010-09-11
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Polytropes Stability Action principle Cosmology Astronomy, Astrophysics and Cosmology Differential Geometry Classical and Quantum Gravitation, Relativity Theory Theoretical, Mathematical and Computational Physics Quantum Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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